## Midterm for Math 151A

The midterm will essentially cover all the material covered in class until Feb. 7. This is chapter 1 (Sec. 1.2), chapter 2 (Secs. 2.1 - 2.4), and chapter 3 (most of sec 3.1), of the textbook.
In general, you should be able to do problems that are similar to the theory problems in the homeworks. In general, you will not have to remember theorems (or the proofs), but certain results/implications of theorems (see below). You might be asked to derive or proof a certain expression, but in that case I will give sufficient hints.

The midterm as well as the final will be with closed books and notes! You can (and might want to) use a calculator.

### Here is a list of things you should know for the midterm (and also for the final)

• Bisectional Method: What is it ? How do we use it (algorithm) ? Error estimate (absolute vs. relative tolerance)!
• Fixed Point Method: What is it ? How do we use it (algorithm) ?
• Newton's Method: What is it ? How do we use it (algorithm) ? Graphic interpretation ? Relation to (derivation from) Taylor expansion.
• Secant Method: What is it ? How do we use it (algorithm) ? Relation to Newton's Method ?
• Rate or Order of Convergence.
• How are numbers represented in binary format (i.e., what is the sign, exponent, mantissa) ?
• What is roundoff ? Chopping vs. Rounding.
• Form of Lagrange polynomial and error term.
• Algorithm to calculate Lagrange polynomials.